EVALUATION OF RESPONSE REDUCTION FACTOR OF RC FRAMED BUILDINGS BY PUSHOVER ANALYSIS

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1 EVALUATION OF RESPONSE REDUCTION FACTOR OF RC FRAMED BUILDINGS BY PUSHOVER ANALYSIS 1 VENKATA RAMANA R. L., 2 INGLE R. K. 1 M.Tech. Student, 2 Professor, Department of Applied Mechanics, VNIT, Nagpur, India 1 venkatlekkala7@gmail.com, 2 rkingle@rediffmail.com Abstract- Vulnerability of buildings to seismic hazards is more drastic in developing countries with high seismicity, as compared to developed countries which is primarily due to the lack of seismic design guidelines. Response Reduction Factor (R) is an essential seismic design tool, which is typically used to describe the level of inelasticity expected in structure during an earthquake. The concept of R factor is based on the observations that well detailed seismic framing systems can sustain large inelastic deformations without collapse through excess of lateral strength over design strength and ductility. Developed countries like United States and Europe, defining R factor with component wise like over strength factor and redundancy factor. Where as in IS 1893 (Part-II) 2002, the R factor which is arrived at empirically based on engineering judgment and perceived earthquake damage with little technical basis. This research focuses on estimating the actual value of R factor of RC framed buildings designed and detailed following the Indian standards and comparing these values with the value suggested in the Indian code. The main focus of this study is to evaluate component wise computation of R factor and effect of number of storeys on this factor using Pushover analysis. Performance level considered in this study is corresponding to global performance level (at 2% storey drift) and local performance level (life safety level) whichever occurs first. From this study, it was found that Indian seismic code giving conservative R value for regular RC framed buildings as per considered performance level. Also found that overstrength factor is decreasing and ductility factor is increasing as the number of sroreys increases. Keywords- Response reduction factor, Over strength factor, Ductility factor and Pushover analysis I. INTRODUCTION Design requirements for lateral loads, such as winds or earthquakes are inherently different from those for gravity (dead and live) loads. Due to frequency of loading scenario, design for wind loads is a primary requirement. But in areas of high seismicity, structures are designed to withstand seismic actions also. Since the seismic design deals with events with lower probability of occurrence, it may therefore be highly uneconomical to design structures to withstand earthquakes for the performance levels used for wind design. Therefore, seismic design uses the concepts of controlled damage and collapse prevention. In this approach, the design base shear (V ) is derived by dividing the elastic baseshear demand (V ) by a factor R (see Eq.1). V = (1) II. COMPONENTS OF R FACTOR From Fig.1, R factor is depends on ductility factor (Rµ), over strength factor (R ) and redundancy factor (R )and it is can be represented by Eq.2. R =R R µ R (2) Fig.1 Base Shear versus Roof Displacement A. Over Strength Factor (R s ) During earhquake, the first significant yield in a RC structure starts at higher than the prescribed unfactored base shear force (see Eq.3) because of the factors given below. i. Code-prescribed load factor and material safety factors used in design. ii. Confinement of concrete, non -structural elements (like infill walls) and special iii. ductility requirements. The lower gravity load applied at the time of the seismic event than the factored gravity loads used in design etc. R = (3) B. Ductility Reduction Factor (Rµ) The displacement ductility ratio is generally defined as the ratio of ultimate displacement ( ) to yield displacement ( ). The ductility reduction factor (Rµ) takes advantage of the energy dissipating capacity of properly designed and well-detailed structures.the ductility reduction factor (Rµ) is a factor which reduces the elastic force demand to the level of idealized yield strength of the structure and, hence, it may be represented by Eq.4. Rµ = (4) Newmark and Hall (1982) was made the first attempt to relate Rµ with µ for a single-degree-offreedom system with elastic-perfectly plastic curve and this relation is shown by Eq.5, Eq.6 and Eq.7 for short, medium and long period buildings respectively. For frequencies above 33 Hz 100

2 Rµ =1 (5) For frequencies between 2 Hz and 8 Hz Rµ = 2µ 1 (6) For frequencies less than 1Hz Rµ =µ (7) A. Material Nonlinearity Mander s confined and unconfined stress-strain curve model has been used in this study to account conrete material nonlinearity (see Fig.2). Bilinearised stress strain model shown in Fig.3 is used for reinforcement steel. C. Redundancy Factor (R R ) Structure with high redundancy can resist more seismic force than structure with less redundancy. Yielding at one location in the structure does not imply yielding of the structure as a whole. Hence the load distribution, due to redundancy of the structure, provides additional safety margin. It is represented by Eq.8. In this study the redundancy factor is taken as unity. R = (8) III. PERFORMANCE LEVEL The Response reduction factor (R) mainly depends on the performance limit state of the structure. The Indian standard IS 1893 does not specify the limit state corresponding to which values of R is recommended. The local performance levels are based on the displacement and rotations of different elements (beams, columns etc.) and shown in Table 1. Table 1 Local Performance Limits-FEMA 356 Fig.2 Concrete Stress-Strain Model (Mander 1988) For concrete ultimate unconfined strain (Єcu) of and ultimate confined strain (Єcc) recommend by ATC-40 has been used in this study (see Eq.9). The value of Єcc is limited to 0.02 to avoid buckling of longitudinal reinforcement. Monotonic coupon test results shall not be used to determine ultimate strain limits because material will fail at low strains due to cyclic effect. For steel ultimate tensile strain of 0.05 and compressive strain of 0.02 is recommended by ASCE Єcc = (9) The global limits typically include requirements for the vertical load capacity, lateral load resistance and lateral drift. For example, the various performance levels in FEMA-356 are specified in terms of the maximum interstorey drift ratio (see Table 2). Table 2 Global Performance Limits-FEMA 356 IV. NONLINEAR MODELLING Non-linear static analysis requires the knowledge of material stress-strain model, plastic hinge property, plastic hinge length and moment-curvature relationship. And also estimation of R values is depends mainly on how well the nonlinear behaviour of frames are modelled in analysis. Fig.3 Idealized Stress-Strain Curve of Fe 415 Steel B. Geometric Nonlinearity The nonlinear behaviour of the frame depends on moment rotation of its members, which in turn depends on the moment curvature characteristics of the plastic hinge section. The plastic rotation capacity (θ ) in a reinforced concrete member depends on the ultimate curvature (ɸ ) and the yield curvature (ɸ ) of the section and the length of the plastic hinge region (Lp). Eq.10 and Eq.11 are used for calculating plastic rotation (θ ). θ = (ɸ ɸ ) l (1-.. ) (10) 101

3 L = 0.08Z d f 0.044d f (11) Idealized Momen-Rotation shown in Fig.4 is used for defining nonlinear hinge property of RC members. Fig.4 Moment-Rotation of Typical Plastic Hinge Fig.6 Plan C. Initial Stiffness of RC Members For regions other than plastic hinging occurs, cracking is expected therefore use of cracked stiffness is customary. Table3 showsvalues of effective stiffness of RC members to use in nonlinear analysis recommended by FEMA-356. Table 3 Initial Stiffness-FEMA 356 Fig.7 (a) Elevation IV. DESCRIPTION OF THE STRUCTURAL SYSTEMS The structural systems considered in this research are shown in Fig.5 intended for office purpose. It is assumed that infill walls are located only at external faces and infill walls contain large openings to avoid the effect of infill walls on R factor. Since the ductility factor mainly depends on the time period of the building, totally four models of building (three, five, eight and twelve Storey buildings) are considered which covers medium and long time period ranges of Indian Response Spectrum. The plan and elevation of considered buildings is shown in Fig.6 and Fig.7. Plan is kept same for all considered buildings.the RC design of these Special Moment Resisting Frame buildings are based on based on IS 456 and IS Fig.7 (b) Elevation Details shown in Table 4 is common to all buildings. Effect of zone on R factor is not considerd in this study and all buildings are assumed to locate in zone IV. Table 4 Common Details of Considered Buildings Fig.5 Response Spectra-Medium Soil (IS ) 102

4 C-Concrete and M-Masonry Since the considered buildings have only external infill walls and also contains large opening areas, the time period is calculated by Eq.12 which does not consider infill walls effect.seismic demands are calculated as per IS 1893 (part-1)-2002 and shown in Table5. T = h. (12) Table 5Seismic Details of Considered Building Fig.8 Pushover Curve of 3 Storey Building Since all the buildings are regular and have major participation mass ratio in fundamental mode (see Table 6), equivalent lateral force distribution (see Eq.13) adopted for this pushover analysis is as suggested in IS 1893 (part 1) F = V (13) Table.6 Mass Participation Ratio of Considered Buildings Fig.9 Pushover Curve of 5 Storey Building In this study, strong column and weak beam criteria is not considered. Modelling of shear hinges is not done beacause from the literature it was found that shear design as per IS ensures that shear failure does not initiate before the formation flexural plastic hinges at member ends.performance level considered in this study is corresponding to global performance level (at 2% storey drift) and local performance level (life safety level) whichever occurs first. Fig.10 Pushover Curve of 8 Storey Building V. R FACTOR EVALUATION Gravity loadcase of D.L+0.5L.L and pushover loadcase shown in Eq.13 is defined as nonlinear load case and developed pushover curvesfor all considered buildings and shown in Fig.8 to Fig.11.P.L refers to Performance Level. Fig.11 Pushover Curve of 12 Storey Building RC Section Details and Plastic Rotation Capacity of Members Materials and sizes of beams and columns used for different storeys is shown in Table 7. Reinforcement details and plastic rotation of beams and columns of 3 storey building only is presented in Table 8. Reinforcement details is given near joints only as the nonlinear modelling is done only at ends of beam and columns. In case of 103

5 columns to consider effect of axial load, plastic rotation is calculated for different axial loads (see Table 10) and for plastic rotation of beams shown in Table8. Table 7Material and RC Section Details of Cosidered Building Table 8 Longitudinal Reinforcement Details of 3 Storey Building Table 9 Plastic Rotation ( θ p ) of Beamsof 3 Storey Building Table 10 Plastic Rotation ( θ p ) of Columns of 3 Storey Building From the pushover curves, parameters shown in Table 11 has been obtained and and are ultimate displacements corresponds to local and global performance levels respectively. R factor and its components has been calculated for all considered buildings and shown in Table

6 Table 11 Pushover Parameters ductility factor contribution to R factor is more in higher storeys. Table 12 R Factors and its Components where N = number of stories VI. RESULTS AND DISCUSSIONS i. The over strength factor is decreasing as the number of stories increases (see Fig.12 and Fig.13) due to high gravity loads to seismic loads ratio in case of lower stories. Fig.12 Ductility Factor versus No.of Storeys ii. The ductility factor is increasing as the number of stories increases due to increase of flexibility of building as number of storeys increases. iii. Fig.13 Over Strength versus No.of Storeys From the Fig.14, contribution of overstrength factor to R factor is more in lower storeys and iv. Fig.14 R factor and its Components in x Direction From the Table 11, it is observed that local performance level is the governing performance level in most of the cases. CONCLUSIONS Based on above study, following conclusions can be summarised. 1. Response Reduction Factor (R) is mainly depending on performance level of the building and both local and global performance level should be considered for evaluating appropriate R factor. 2. The over strength factor is decreasing and ductility factor is increasing as the number of stories increases. 3. The maximum ductility provided by the special moment resisting frame is about 3 for the considered performance level. 4. According to considered performance level, Indian code giving conservative R value for regular RC framed buildings. REFERENCES [1] Applied Technology Council (ATC) Seismic evaluation and retrofit of concrete buildings. Rep. No. ATC-40, Redwood City, California. [2] American Society of Civil Engineers (ASCE) Prestandard and commentary on the seismic rehabilitation of buildings. Rep. No. FEMA-356, Washington, D.C. [3] Bureau of Indian Standards (BIS) Criteria for earthquake resistant design of structures. Rep. No. IS- 1893, Part-1, New Delhi, India. [4] Mander, J. B., Priestley, M. J. N., and Park, R. (1988). "Observed stress-strain behavior of confined concrete." J. Struct. Eng., ASCE, 114(8), [5] Mondal, A., Ghosh, S., and Reddy, G. (2013). Performance based evaluation of the response reduction factor for ductile RC frames. J. Struct. Eng., 56, [6] Whittaker, A., Hart, G., and Rojahn, C. (1999). Seismic response modification factors. J. Struct. Eng., 125(4),